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D0-D0 Mixing
Michael D. Sokoloff
University of Cincinnati
The oscillation in time of neutral D mesons into their antiparticles, and
vice versa, commonly called D0-D0 mixing, has been observed by several
experiments in a variety of channels during the past year. While K0-K0
mixing and B0-B0 mixing are (relatively) well understood in the Standard
Model of particle physics, the observations of D0-D0 mixing indicate that
the physical eigenstates have decay rate differences and/or mass
differences greater than expected most naively. In this talk I will discuss
the recent experimental results and the extent to which they probe nonperturbative QCD and physics beyond the Standard Model.
1
The Nature of Particle Physics
•
Particle physicists study the fundamental constituents of matter
and their interactions.
•
Our understanding of these issues is built upon certain
fundmental principles
– The laws of physics are the same everywhere
– The laws of physics are the same at all times
– The laws of physics are the same in all inertial reference
systems (the special theory of relativity)
– The laws of physics should describe how the wave function
of a system evolves in time (quantum mechanics)
•
These principles do not tell us what types of fundamental
particles exist, or how they interact, but they restrict the
types of theories that are allowed by Nature.
•
In the past 30 years we have developed a Standard Model of
particle phyiscs to describe the electromagnetic, weak nuclear,
and strong nuclear interactions of constituents in terms of
quantum field theories. In addition to the particles and forces
of the Standard Model, there must be New Physics, also called
Physics Beyond the Standard Model.
2
Special Relativity
•
Energy and Momentum
– Energy and momentum form a four-vector (E,px,py,pz).
The Lorentz invariant quantity defined by energy and
momentum is mass:
– For the special case when an
object is at rest so that its
momentum is zero
•
When a particle decays, we can measure the energy and
momenta of it decay products (the daughters), albeit
imperfectly. From these, we calculate the energy and
momentum of the parent.
From the reconstructed
energy and momentum of the
candidate parent, we
calculate its invariant mass.
3
Classical Field Theory (E&M)
4
Fields and Quanta
•
•
•
•
•
Electromagnetic fields transfer energy and momentum
from one charged particle to another.
Electromagnetic energy/momentum is quantized:
– E = hn ; p = hn/c
These quanta are called photons: g
In relativistic quantum field theory: Am
g
To calculate cross-sections and decay rates we use
perturbation theory based on Feynman Diagrams:
5
Strong Nuclear Interactions of Quarks and Gluons
Each quark carries one of three strong charges, and each
antiquark carries an anticharge. For convenience, we call
these colors:
Just as photons are the quanta of EM fields, gluons are the
quanta of strong nuclear fields; however, while photons are
electrically neutral, gluons carry color-anticolor quantum
numbers.
The Nobel Prize in
Physics 2004
Gross
Politzer
Wilczek
6
Baryons and Mesons
• Quarks are never observed as free particles.
– Baryons consist of three quarks, each with a different
color (strong nuclear) charge
proton =
neutron =
– Mesons consist of quark-antiquark pairs with canceling
color-anticolor charges
• Baryons and meson (collectively known as hadrons) have
net color charge zero.
• A Van der Waals-types of strong interaction creates an
attractive force which extends a short distance (~ 1 fm)
to bind nucleii together.
7
Weak Charged Current Interactions
neutrino scattering
charm decay
f
~
f
As a first approximation, the weak charged
current interaction couples fermions of the same
generation. The Standard Model explains
couplings between quark generations in terms of
the Cabibbo-Kobayashi-Maskawa (CKM) matirx.
8
Weak Phases in the Standard Model
b = f1; a = f2; g = f3
9
Charm Meson Mixing
Why is observing charm mixing interesting?
It completes the picture of quark mixing already seen in the
K, Bd, and Bs systems.
K — PR 103, 1901 (1956); PR 103, 1904 (1956).
Bd — PL B186, 247 (1987); PL B192, 245 (1987).
Bs — PRL 97, 021802 (2006); PRL 97, 242003 (2006).
In the Standard Model, it relates to processes with downtype quarks in the mixing loop diagram.
It is a significant step toward observation of CP violation in
the charm sector.
It could indicate new physics.
10
Mixing Phenomenology
Neutral D mesons are produced
as flavor eigenstates D0 and D0
and decay via
D1, D2 have masses M1, M2 and
widths 1, 2
Mixing occurs when there is a
non-zero mass
or lifetime difference
as mass, lifetime eigenstates D1,
D2
where
and
For convenience define, x and y
where
and define the mixing rate
( < 5 x 10-4 )
11
How Mixing is Calculated
12
Standard Model Mixing Predictions
Box diagram SM charm mixing
rate naively expected to be
very low (RM~10-10) (Datta &
Kumbhakar)
Z.Phys. C27, 515 (1985)
CKM suppression → |VubV*cb|2
GIM suppression → (m2s-m2d)/m2W
Di-penguin mixing, RM~10-10
Phys. Rev. D 56, 1685 (1997)
Enhanced rate SM calculations
generally due to long-distance
contributions:
first discussion, L. Wolfenstein
Phys. Lett. B 164, 170 (1985)
13
Standard Model Mixing Predictions
Box diagram SM charm mixing
rate naively expected to be
very low (RM~10-10) (Datta &
Kumbhakar)
Z.Phys. C27, 515 (1985)
CKM suppression → |VubV*cb|2
GIM suppression → (m2s-m2d)/m2W
Di-penguin mixing, RM~10-10
Phys. Rev. D 56, 1685 (1997)
Enhanced rate SM calculations
generally due to long-distance
contributions:
first discussion, L. Wolfenstein
Phys. Lett. B 164, 170 (1985)
Partial History of LongDistance Calculations
• Early SM calculations indicated
long distance contributions
produce x<<10-2:
– x~10-3 (dispersive sector)
• PRD 33, 179 (1986)
– x~10-5 (HQET)
• Phys. Lett. B 297, 353 (1992)
• Nucl. Phys. B403, 605 (1993)
• More recent SM predictions
can accommodate x, y ~1% [of
opposite sign] (Falk et al.)
– x,y ≈ sin2 qC x [SU(3) breaking]2
• Phys.Rev. D 65, 054034 (2002)
• Phys.Rev. D 69, 114021 (2004)
14
New Physics Mixing Predictions
Possible enhancements to mixing due to • Large possible SM contributions to
new particles and interactions in new
mixing require observation of either a
physics models
CP-violating signal or | x | >> | y | to
Most new physics predictions for x
establish presence of NP
Extended Higgs, tree-level FCNC
• A recent survey (arXiv:0705.365v1)
Fourth generation down-type quarks
summarizes models and constraints:
Supersymmetry: gluinos, squarks
Lepto-quarks
Fourth generation
Vector leptoquarks
Q = -1/3 singlet
quark
Flavor-conserving
Two-Higgs
Q = +2/3 singlet
quark
Flavor-changing
neutral Higgs
Little Higgs
Scalar leptoquarks
Generic Z’
MSSM
Left-right
symmetric
Heavy weak iso-singlet quarks
Supersymmetric
alignment
and more
15
Time-Evolution of D0K Decays
RS = CF
DCS and mixing amplitudes
interfere to give a “quadratic”
WS decay rate (x, y << 1):
WS = DCS
DCS
K+-
D0
D0
where
and  is the phase difference between DCS and CF decays.
16
D0

K Reconstruction
384 fb-1 e+e-  c,c
Slow pion charge tags neutral
D production flavor
Beam spot:
x ≈ 100 mm
y ≈
7 mm
17
Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
18
Simplified Fit Strategy & Validation
Fit m(K) and Dm in bins of time:
 If no mixing, ratio of WS to RS
signal should be constant
 No assumptions made on time
evolution of background
 Each time bin is fit independently
WS (0.75<t<2.5 ps)
m(K+–)
Time bins:
WS (0.75<t<2.5 ps)
Dm
19
Simplified Fit Strategy & Validation
Rate of WS events clearly increases with time:
WS/RS (%)
(stat. only)
20
Simplified Fit Strategy & Validation
Rate of WS events clearly increases with time:
WS/RS (%)
(stat. only)
Inconsistent
with no-mixing
hypothesis:
2=24
21
Simplified Fit Strategy & Validation
Rate of WS events clearly increases with time:
WS/RS (%)
(stat. only)
Consistent with
prediction from
full likelihood fit
2=1.5
Inconsistent
with no-mixing
hypothesis:
2=24
22
Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
23
m(K)-Dm Fit Results
Signal = 1 141 500 ± 1 200
Signal = 4 030 ± 90
24
Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
25
Decay Time Resolution
Average D0 flight length is twice average resolution
Resolution function described by sum of 3 Gaussians
Resolution widths scales with t
Mean of core Gaussian allowed to be non-zero
Observed core Gaussian shifted 3.6±0.6fs
=
For combinatorial background, use Gaussians and
power-law “tail” for small long-lived component
26
RS Decay Time Fit
RS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
D0 lifetime and resolution function
fitted in RS sample:
 = 410.3±0.6 (stat.) fs
Consistent with PDG (410.1±1.5 fs)
NB: Shifted core Gaussian dominates systematic uncertainties
27
Full Fit Procedure
Unbinned maximum likelihood fit in several steps
(fitting 1+ million events takes a long time)
Fit to m(K) and Dm distribution:
RS and WS samples fit simultaneously
Signal and some background parameters shared
All parameters determined in fit to data, not MC
Fit RS decay time distribution:
Determines D0 lifetime and resolution function
Include event-by-event decay time error t in resolution
Use m(K) and Dm to separate signal/bkgd (fixed shapes)
Fit WS decay time distribution:
Use D0 lifetime and resolution function from RS fit
Compare fit with and without mixing (and CP violation)
28
WS Fit with no Mixing
WS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
data - no mix PDF
Fit result assuming no mixing:
RD: (3.53±0.08±0.04)x10-3
29
WS Fit with no Mixing
WS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
data - no mix PDF
Fit result assuming no mixing:
poor fit
RD: (3.53±0.08±0.04)x10-3
30
WS Fit with Mixing
WS decay time, signal region
plot signal region:
1.843<m<1.883 GeV/c2
0.1445<Dm< 0.1465 GeV/c2
Fit results allowing mixing:
RD: (3.03±0.16±0.10)x10-3
x’2: (-0.22±0.30±0.21)x10-3
y’: (9.7±4.4±3.1)x10-3
data - no mix PDF
fine fit
31
Signal Significance
Significance calculated from change in log likelihood:
(stat. only)
Best fit
1
2
3
4
No mixing
5
32
Signal Significance
Significance calculated from change in log likelihood:
(stat. only)
Best fit
1
Corresponds to 4.5
(with 2 parameters)
2
3
4
No mixing
5
33
Signal Significance
Best fit is in unphysical region (x'2<0)
(stat. only)
Best fit
Physical solution
(y'=6.4x10-3)
1
Corresponds to 4.5
(with 2 parameters)
2
3
4
No mixing
5
34
Signal Significance with Systematics
Including systematics (~ 0.7 x stat)
decreases signal significance
[ PRL. 98, 211802 (2007) ]
Best fit
1
2
3
Fit is inconsistent
with no-mixing at 3.9 No mixing
4
5
35
K Analysis from Belle
Last year Belle published
analysis of K decays:
PRL 96,151801
Results consistent within 2:
400 fb-1
stat. only
BaBar 1
BaBar 2
BaBar 3
no-mixing
excluded at 2
(0,0)
Belle 2 statistical
36
Average K Mixing Results
Heavy flavor averaging group (HFAG)
provides “official” averages
Combine BaBar and Belle likelihoods in 3 dimensions (RD, x'2,y')
May 2007 Averages:
+0.14
RD: (3.30 -0.12 )
x 10-3
x’2: (-0.01±0.20) x 10-3
y’ :
+2.8
(5.5 -3.7
)x
10-3
1
y'
2
No mixing
excluded > 4
x'2
3
4
5
37
Preliminary Kπ Mixing Results from CDF
Best fit for mixing parameters
(uncertainties are combined
stat. and systematic)
• Fit 2 = 19.2 for 17 dof
• 3.8  from Null Hypothesis
RD: (3.04 ± 0.55 ) x 10-3
x’2: (-0.12 ± 0.35) x 10-3
y’ : (8.5 ± 7.6 ) x 10-3
38
D in D0 → h+h[ PRL. 91, 121801 (2003) ]
39
BaBar’s Early D in D0 → h+h[ PRL. 91, 121801 (2003) ]
91 fb-1
40
Belle’s Recent D in D0 → h+h[ PRL. 98, 211803 (2007) ]
540 fb-1
Ave
(1.12 ± 0.32)%
41
BaBar’s Preliminary D D0 → h+h-
42
D0 → h+h- : Results
Babar’s preliminary 384 fb-1 results
Combining KK and  results gives
yCP = (1.24 ± 0.39 ± 0.13)%
CP violation consistent with zero.
BaBar
Tagged
(preliminary)
(1.24 ± 0.39 ±0.13)%
BaBar
Untagged (91 fb-1)
(0.2 ± 0.4 ± 0.5)%
BaBar
Combined
(0.94 ± 0.35)%
Belle
Tagged
(1.31 ± 0.32 ± 0.25)%
BaBar + Belle
Combined
(1.10 ± 0.27)%
43
Mixing in D0 → KSπ+π-
44
Mixing in D0 → KSπ+πX : (0.80 ± 0.35 ± 0.15)%
y : (0.33 ± 0.24 ± 0.14)%
(assuming no CP violation)
95% CL
contours
45
Mixing in D0 → K+-0
1483 ± 56 signal events
“Wrong-sign” decay rate varies
across the Dalitz plot:
DCS term
Resonance phase
Interference term
CF (mixed) term
Phase between
RS and WS
Subscript D indicates dependence
on position in the Dalitz plot.
Yields from 384 fb-1
Bad charm
Combinatorics
46
D0 → K+-0 : Results
No mixing is excluded at
the 99% confidence level.
Stat+syst
x’’: (2.39 ± 0.61 ± 0.32) %
Y’’ : (-0.14 ± 0.60 ± 0.40 )%
RM: (2.9 ± 1.6) x 10-4
68.3%
95.0%
99.0%
99.9%
47
20 Years Ago
48
10 Years Ago
RM < 0.92% , no int.
RM < 3.6%, int allowed
RM < 0.50% , semi-lep
RM < 0.85%, CPV allowed in int.
RDCSD = (0.68 ± 0.34 ±0.07) %
RDCSD = (0.68 ± 0.34 ±0.07) %
y = (0.5 ± 1.5 ± syst.) %
results on the way
49
Today
HFAG
D0 → Kπ
RD: (3.30
+0.14
-0.12
) x 10-3
x’2: (-0.01±0.20) x 10-3
+2.8
y’ : (5.5
) x 10-3
-3.7
y'
No mixing
excluded > 4
x'2
CDF
D 0 → K Sπ+ π-
D 0 → K + π- π0
Belle
Stat+syst
D in D0 → h+hBaBar + Belle
(1.10 ± 0.27)%
95% CL contours
68.3%
95.0%
99.0%
99.9%
50
10 Years From Now ??
My guesstimates of what we can do, assuming 100 fb-1 from
LHCb and 50 ab-1 from SuperB, in units of 10-4
x
y
YCP
Kπ
h +h -
KSπ+π-
y’
0.2
5
x’’
y’’
8
8
5
5
5
K+π-π0
π-π+π0
(x’)2
7
7
BES III should be able to measure cos  ±
3 III will measure SCS branching fractions with 5%
SuperB and BES
fractional precision, constraining Standard Model contributions to x & y.
Altogether, D0-D0 mixing measurements, and measurements of CPviolation in mixing, will provide insights into physics beyond the SM
that will complement direct observations made at the LHC.
51
Allowing for CP Violation
CP violation could introduce different time
dependences for D0 (+) and D0 (-):
Three possible types of CP violation:
Direct CP violation in DCS decay
CP violation in mixing
CP violation in interference between mixing and decay
Simpler to fit D0 (+) and D0 (-) separately:
CP violation if one or more “±” parameters are different
52
CPV Allowed Contours
Results of fitting D0 and D0 separately:
x'+2: (-0.24±0.43±0.30)x10-3
y'+: (9.8±6.4±4.5)x10-3
x'-2: (-0.20±0.41±0.29)x10-3
y'-: (9.6±6.1±4.3)x10-3
AD=(-2.1±5.2±1.5)%
D0
D0
No evidence for CP violation found
53